We compare the single-particle plasmonic sensitivity of silver and gold nanorods with similar resonance wavelengths by monitoring the plasmon resonance shift upon changing the environment from water to 12.5% sucrose solution. We find that silver nanoparticles have 1.2 to 2 times higher sensitivity than gold, in good agreement with simulations based on the boundary-elements-method (BEM). To exclude the effect of particle volume on sensitivity, we test gold rods with increasing particle width at a given resonance wavelength. Using the Drude-model of optical properties of metals together with the quasi-static approximation (QSA) for localized surface plasmons, we show that the dominant contribution to higher sensitivity of silver is the lower background polarizability of the d-band electrons and provide a simple formula for the sensitivity. We improve the reversibility of the silver nanorod sensors upon repeated cycles of environmental changes by blocking the high energy parts of the illumination light.